public void TestFindingMinimumSpanningTree()
{
// Item1 - the vertices to add to the graph
// Item2 - the adjacency matrix that defines the edges
// of the graph.
// Item3 - expected MST weight
Tuple <string[], float?[, ], float>[] test_vectors =
{
new Tuple <string[], float?[, ], float>(
new string[] { "A" },
new float?[, ] {
{ null }
},
0f),
new Tuple <string[], float?[, ], float>(
new string[] { "A","B" },
new float?[, ]
{
{ null, 5.0f },
{ 5.0f, null }
},
5f),
new Tuple <string[], float?[, ], float>(
new string[] { "A","B", "C", "D", "E", "F", "G", "H", "I", "J" },
new float?[, ]
{
{ null, 2f, 4f, 4f, null, null, null, null, null, null },
{ 2f, null, 3f, null, 7f, null, null, null, null, null },
{ 4f, 3f, null, 1f, 8f, 9f, null, null, null, null },
{ 4f, null, 1f, null, null, 10f, null, null, null, null },
{ null, 7f, 8f, null, null, null, 3f, 11f, null, null },
{ null, null, 9f, 10f, null, null, null, null, 6f, null },
{ null, null, null, null, 3f, null, null, null, 6f, null },
{ null, null, null, null, 11f, null, null, null, 1f, 2f },
{ null, null, null, null, null, 6f, 6f, 1f, null, 5f },
{ null, null, null, null, null, null, null, 2f, 5f, null }
},
31f),
new Tuple <string[], float?[, ], float>(
new string[] { "A","B", "C", "D", "E", "F", "G", "H", "I", "J", "K"},
new float?[, ]
{
{ null, null, 3f, null, null, 2f, null, null, null, null, 1f},
{ null, null, 7f, null, 3f, 3f, null, null, null,8f, null },
{ 3f, 7f, null, null, null, 10f, null, null, 2f, null, 1f},
{ null, null, null, null, null, null, null, null, null,5f, null },
{ null, 3f, null, null, null, null, null, 4f, 1f, null, 7f},
{ 2f, 3f, 10f, null, null, null, null, null, null,4f, null },
{ null, null, null, null, null, null, null, 7f, 5f, null, 9f},
{ null, null, null, null, 4f, null, 7f, null, null, null, null},
{ null, null, 2f, null, 1f, null, 5f, null, null, null, null},
{ null, 8f, null, 5f, null, 4f, null, null, null, null, null},
{ 1f, null, 1f, null, 7f, null, 9f, null, null, null, null}
},
28f)
};
foreach (var test_vector in test_vectors)
{
var graph = new UndirectedWeightedGraph <string>(3);
// Sanity check
Assert.AreEqual(test_vector.Item1.Length, test_vector.Item2.GetLength(0));
Assert.AreEqual(test_vector.Item1.Length, test_vector.Item2.GetLength(1));
// Add vertices
foreach (var vertex in test_vector.Item1)
{
graph.AddVertex(vertex);
}
// Assert that the graph size is as expected
Assert.AreEqual(test_vector.Item1.Length, graph.Size);
// Add edges. Iterate over the upper triangular matrix only
// as the lower triangular matrix (below the diagonal) must
// be its mirror.
for (int row = 0; row < test_vector.Item1.Length; ++row)
{
for (int col = row + 1; col < test_vector.Item1.Length; ++col)
{
// Sanity check
Assert.AreEqual(test_vector.Item2[row, col], test_vector.Item2[col, row]);
if (test_vector.Item2[row, col] != null)
{
graph.AddEdge(row, col, test_vector.Item2[row, col].Value);
}
}
}
// Compute the MST
IWeightedGraph <string> mst = graph.FindMinimumSpanningTree();
// Assert that the size of the produced MST is expected
Assert.AreEqual(test_vector.Item1.Length, mst.Size);
// A vertex is 'marked' when we encounter an edge that starts
// or ends in a given vertex. All vertices must be marked in
// the end.
bool[] marked_vertices = new bool[test_vector.Item1.Length];
// The number of discovered edges (bidirectional edges are
// count only once). The number of edges in an MST must be
// equal to the number of vertices minus one.
int edge_count = 0;
// The total weight of the MST.
float mst_weight = 0.0f;
// Iterate over the upper triangular matrix only. The lower
// triangular matrix must be a mirror of it.
for (int row = 0; row < test_vector.Item1.Length; ++row)
{
for (int col = row + 1; col < test_vector.Item1.Length; ++col)
{
// If (row, col) edge exists in MST, (col, row) must exist
// as well as this is an undirected graph
Assert.AreEqual(mst.EdgeExists(row, col), mst.EdgeExists(col, row));
if (mst.EdgeExists(row, col))
{
// If the edge exists in MST, it must also exist in the
// original graph
Assert.IsTrue(graph.EdgeExists(row, col));
// Assert that the weight of (row, col) edge equals
// the weight of that edge in the original graph
Assert.AreEqual(graph.GetEdgeWeight(row, col), mst.GetEdgeWeight(row, col));
// Assert that (col, row) edge weight matches the (row, col)
// edge weight (must be the case as this is an undirected
// graph).
Assert.AreEqual(mst.GetEdgeWeight(row, col), mst.GetEdgeWeight(col, row));
// 'Mark' the start and end vertices
marked_vertices[row] = marked_vertices[col] = true;
// Add to the total mst weight
mst_weight += mst.GetEdgeWeight(row, col);
// Increment the number of discovered edges
++edge_count;
}
}
}
// If all of the following asserts pass, the generated graph
// is in fact a MST
if (test_vector.Item1.Length > 1)
{
// Assert that every vertex has been marked
foreach (var marked in marked_vertices)
{
Assert.IsTrue(marked);
}
}
// Assert that the number of discovered edges is one less than
// the number of vertices in the graph
Assert.AreEqual(test_vector.Item1.Length - 1, edge_count);
// Assert that the total MST weight matches the expected weight
Assert.That(
test_vector.Item3,
Is.EqualTo(mst_weight).Within(1).Ulps);
}
}
public void TestFindingMinimumSpanningTreeWithDisconnectedGraph()
{
// Item1 - the vertices to add to the graph
// Item2 - the adjacency matrix that defines the edges
// of the graph.
Tuple <string[], float?[, ]>[] test_vectors =
{
new Tuple <string[], float?[, ]>(
new string[] { "A","B" },
new float?[, ]
{
{ null, null },
{ null, null }
}),
new Tuple <string[], float?[, ]>(
new string[] { "A","B", "C", "D", "E", "F", "G", "H", "I", "J" },
new float?[, ]
{
{ null, 2f, 4f, 4f, null, null, null, null, null, null },
{ 2f, null, 3f, null, null, null, null, null, null, null },
{ 4f, 3f, null, 1f, null, null, null, null, null, null },
{ 4f, null, 1f, null, null, null, null, null, null, null },
{ null, null, null, null, null, null, 3f, 11f, null, null },
{ null, null, null, null, null, null, null, null, 6f, null },
{ null, null, null, null, 3f, null, null, null, 6f, null },
{ null, null, null, null, 11f, null, null, null, 1f, 2f },
{ null, null, null, null, null, 6f, 6f, 1f, null, 5f },
{ null, null, null, null, null, null, null, 2f, 5f, null }
}),
new Tuple <string[], float?[, ]>(
new string[] { "A","B", "C", "D", "E", "F", "G", "H", "I", "J", "K"},
new float?[, ]
{
{ null, null, 3f, null, null, 2f, null, null, null, null, 1f},
{ null, null, null, null, null, 3f, null, null, null,8f, null },
{ 3f, null, null, null, null, 10f, null, null, null, null, 1f},
{ null, null, null, null, null, null, null, null, null,5f, null },
{ null, null, null, null, null, null, null, 4f, 1f, null, null},
{ 2f, 3f, 10f, null, null, null, null, null, null,4f, null },
{ null, null, null, null, null, null, null, 7f, 5f, null, null},
{ null, null, null, null, 4f, null, 7f, null, null, null, null},
{ null, null, null, null, 1f, null, 5f, null, null, null, null},
{ null, 8f, null, 5f, null, 4f, null, null, null, null, null},
{ 1f, null, 1f, null, null, null, null, null, null, null, null}
})
};
foreach (var test_vector in test_vectors)
{
var graph = new UndirectedWeightedGraph <string>(3);
// Sanity check
Assert.AreEqual(test_vector.Item1.Length, test_vector.Item2.GetLength(0));
Assert.AreEqual(test_vector.Item1.Length, test_vector.Item2.GetLength(1));
// Add vertices
foreach (var vertex in test_vector.Item1)
{
graph.AddVertex(vertex);
}
// Assert that the graph size is as expected
Assert.AreEqual(test_vector.Item1.Length, graph.Size);
// Add edges. Iterate over the upper triangular matrix only
// as the lower triangular matrix (below the diagonal) must
// be its mirror.
for (int row = 0; row < test_vector.Item1.Length; ++row)
{
for (int col = row + 1; col < test_vector.Item1.Length; ++col)
{
// Sanity check
Assert.AreEqual(test_vector.Item2[row, col], test_vector.Item2[col, row]);
if (test_vector.Item2[row, col] != null)
{
graph.AddEdge(row, col, test_vector.Item2[row, col].Value);
}
}
}
// Compute the MST. The method must return a NULL value as the
// graph is disconnected.
Assert.IsNull(graph.FindMinimumSpanningTree());
}
}
public void AssertFindMinimumSpanningTreeThrowsExceptionIfGraphEmpty()
{
var graph = new UndirectedWeightedGraph <int>();
Assert.Throws <InvalidOperationException>(() => graph.FindMinimumSpanningTree());
}